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Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Feb;79(2 Pt 2):026609. Epub 2009 Feb 23.

Stationary and pulsating dissipative light bullets from a collective variable approach.

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  • 1Institut Carnot de Bourgogne, UMR 5209 CNRS, Universit√© de Bourgogne, 9 Avenue Savary, BP 47870, 21078 Dijon Cedex, France.


A collective variable approach is used to map domains of existence for (3+1)-dimensional spatiotemporal soliton solutions of a complex cubic-quintic Ginzburg-Landau equation. A rich variety of evolution behaviors, which include stationary and pulsating dissipative soliton dynamics, is revealed. Comparisons between the results obtained by the semianalytical approach of collective variables, and those obtained by a purely numerical approach show good agreement for a wide range of equation parameters. This also demonstrates the relevance of the semianalytical method for a systematic search of stability domains for spatiotemporal solitons, leading to a dramatic reduction of the computation time.

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